A bag of wheat weighs 200 kg. To what height should it be raised so that its potential energy may be 9800 joules ? (`g = 9.8 ms^(-2)`)

Options

A. 10 m
B. 8 m
C. 5 m
D. 4 m

Explanation

To find the height to which a bag of wheat weighing 200 kg should be raised to achieve a potential energy of 9800 joules, we can use the formula for gravitational potential energy (PE):

\[ PE = m \cdot g \cdot h \]

Where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass (in kg),
- \( g \) is the acceleration due to gravity (in m/s²),
- \( h \) is the height (in meters).

### Step-by-Step Solution:

1. **Identify the known values:**
- Mass \( m = 200 \, \text{kg} \)
- Potential Energy \( PE = 9800 \, \text{J} \)
- Acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \)

2. **Substitute the known values into the potential energy formula:**
\[ 9800 = 200 \cdot 9.8 \cdot h \]

3. **Rearrange the formula to solve for height \( h \):**
\[ h = \frac{PE}{m \cdot g} \]

4. **Plug in the values:**
\[ h = \frac{9800}{200 \cdot 9.8} \]

5. **Calculate the denominator:**
\[ 200 \cdot 9.8 = 1960 \]

6. **Now divide the potential energy by the calculated denominator:**
\[ h = \frac{9800}{1960} \]

7. **Perform the division:**
\[ h = 5 \, \text{m} \]

### Final Answer:
The height to which the bag of wheat should be raised is **5 meters**.